Author(s)

Renqing You¹, Peng Liao^2*

¹School of Mathematics, Yunnan Normal University, Kunming, China.
²School of Mathematics and Statistics, Southwest University, Chongqing, China.

In this paper, we deal with the existence of solution for a class of quasilinear Schrödinger equations with a nonlocal term

Where μ ∈ (0,3), the function K,V ∈ C(R³,R⁺) and V(x) may be vanish at infinity, g is a C¹ even function with g’(t) ≤ 0 for all t ≥ 0, g(0) = 1, , 0 < a < 1, and F is the primitive function of f which is superlinear but subcritical at infinity in the sense of Hardy-littlewood-Sobolev inequality. By the mountain pass theorem, we prove that the above equation has a nontrivial solution.

Quasilinear Schrödinger Equation, Nontrivial Solution, Variational Method

You, R. and Liao, P. (2022) Existence of the Solutions for a Class of Quasilinear Schrödinger Equations with Nonlocal Term. Journal of Applied Mathematics and Physics, 10, 3265-3280. doi: 10.4236/jamp.2022.1011216.